To answer the OPs legality question I feel the an example has existed for some years. Bunk houses. I haven't used many of these but have come across some which rely on users paying simply by leaving the money in a jam jar or similar. At least one of I've visited was run by an organisation I've forgotten the name of but I'm sure there must be rules in place to cover this.
Re tax etc. if someone is running a genuine honesty box operation I'd hope the honesty stretches beyond expecting users to be honest.